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UID:20251121T162510EST-1552TJdUk3@132.216.98.100
DTSTAMP:20251121T212510Z
DESCRIPTION:Title: Perfect bases in representation theory.\n\nAbstract: A f
 amous foundational problem concerns finding combinatorial expressions for 
 tensor products of irreducible representations. A conceptually satisfying 
 way to answer this question is to find bases for representations which res
 trict to bases of tensor product multiplicity spaces. These bases are call
 ed 'good' or 'perfect' and were first proposed 35 years ago by Gelfand and
  Zelevinsky. The construction of such bases is more difficult than one mig
 ht expect and cannot be achieved by elementary means: they require geometr
 ic inputs such as the geometric Satake correspondence (Mirkovic-Vilonen)\,
  or the theory of perverse sheaves on quiver varieties (Lusztig). These le
 ad to the MV basis\, and Lusztig's dual canonical and dual semicanonical b
 ases.\n	Remarkably\, each such perfect basis gives rise to the same combina
 torial structure\, which is encoded as a collection of polytopes. With Pie
 rre Baumann and Allen Knutson\, we defined measures supported on these pol
 ytopes. These measures allow us to perform computations which distinguish 
 among these different bases.\n
DTSTART:20220331T200000Z
DTEND:20220331T210000Z
LOCATION:Room 920\, Burnside Hall\, CA\, QC\, Montreal\, H3A 0B9\, 805 rue 
 Sherbrooke Ouest
SUMMARY:Joel Kamnitzer (University of Toronto)
URL:/mathstat/channels/event/joel-kamnitzer-university
 -toronto-338767
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